CONCRETENESS FADING WITH MONTESSORI MATERIALS TO TEACH MATHEMATICAL EQUIVALENCES IN PRIMARY SCHOOL

Abstract

The research is focused on the teaching of mathematics in elementary school, particularly in the second class. There are two areas of interest: the effectiveness of the use of concrete material and the role of the teaching strategy used to teach. Different variables have been observed through two experimental studies conducted on samples of second class elementary school children. The concept of numerical equivalence was proposed to the children through a series of exercises carried out with the researcher, at the end of which a transfer test was administered. In the first study, three didactic strategies were compared: concrete, abstract / symbolic, concreteness fading. The latter strategy, devised by Bruner in 1966, has recently been studied. The concreteness fading foresees that the teaching of the mathematical concept is taught first through concrete didactic material, then through iconic material, finally through symbolic notation (concrete that fades towards the abstract). Furthermore, two types of didactic material were compared: Montessori and other. The study showed that the children's performance in the transfer test administered at the end of the teaching phase was superior in the group that learned with the concreteness fading strategy. The type of material used had no effect on learning. The second study compared the two concrete and concreteness fading strategies, examining children's performance both at the end of the teaching phase and after two weeks. Furthermore, more varied exercises have been proposed compared to the first study, in order to observe whether the repetition of exercises all similar to each other could cause a limitation in learning. The results show that the children who learned with the concreteness fading strategy benefited from more varied exercises while those who learned with the concrete alone were not affected by the difference. An interesting difference emerges from the results of the first study regarding the time variable. In fact, after two weeks, the children who have learned with the concrete obtain performances similar to those of the concreteness fading group. The research therefore shows us that the use of concrete material in teaching mathematics is effective but requires longer settling times, therefore it is not appropriate to verify it just after teaching. The concreteness fading strategy, on the other hand, seems to guarantee verifiable learning even immediately after teaching, and which remains stable over time.